Therefore, constraints for the maximally entangled state gives maximally mixed reduced density matrix for the smaller of the two bi-partition for every bi-partition of the system. States satisfying these conditions are also know as absolute maximally entangled states [1]}. We have shown that for two qubit system, the Bell states and for three qubit system, the GHZ and GHZ like states satisfy all the constraints, and hence are absolute maximally entangled states. It has been shown that for four qubits and for n-qubit systems (\(n\ge 7\) ), absolutely maximally entangled states do not exist [1]}, hence for such systems, no state exists which satisfies all the constraints. It would be interesting to explore further the absolute maximally entangled states of higher dimensions using the present approach.
